When a timetable for a train or bus system is established, typically, headway times between two stations (standard running nous minute) and dwell times in each station (predefined dwell hour/minute) are determined in advance, and the timetable is created based on such times. In addition, a new timetable for mobiles such as trains is not frequently created. Instead, an existing timetable diagram (hereinafter, referred to as a scheduling diagram) is copied and is then revised on the basis of lessons from experiences. In practice, by repeating the revision, the scheduling diagram is customized.
However, when the scheduling diagram is revised, several problems occur in many cases just by shifting a single schedule line of the scheduling diagram (hereinafter, referred to as a “schedule line”). In particular, this becomes serious when trains are running very densely. Specifically, if a schedule line is shifted in a scheduling diagram visualized on a two-dimensional basis, the schedule lines may overlap with each others, a running sequence may be reversed, or a mismatch problem may occur.
For safe operation of trains, it is necessary to secure sufficient time intervals (headway hour/minute) with preceding and succeeding trains and appropriately maintain intervals between the schedule lines. Furthermore, in order to provide robustness of the scheduling diagram, it is also important to secure a sufficient dwell times or a sufficient layover time at a turnaround station (turnaround layover hour/minute). This is necessary in order to absorb disturbances in the scheduling diagram within the corresponding dwell or layover time. For this reason, generally, in a method of shifting lit a schedule line in a scheduling diagram change work of trains or the like, a reference running hour/minute is not changed basically, and only the dwell or layover time is adjusted.
However, if a dwell time of any train in an intermediate station increases, the increasing time affects the entire scheduling diagram and all other interfering schedule lines, so that a mismatch propagates widely. For this reason, it is desirable to provide a transportation service timetable planner with a rescheduling structure capable of simultaneously shifting other schedule lines by shifting a single schedule line while predefined constant requirements are satisfied.
For example, in the field of train transportation, as a simplified simulation technique, a project evaluation and review technique (PERT) is employed. In addition, a critical path technique is also known to find candidates of schedule lines to be corrected when a delay occurs in the event of a traffic accident. In a significant number of such examples, a method of finding a part that causes violation of the constraint in a chain-reaction manner out of a scheduling scheme such as a train scheduling diagram having various temporal constraints is also employed.
However, in the PERT-based methods knows in the art, only a minimum time interval necessary between events is treated as a constraint. Therefore, they are used limitatively. In the critical path methods, basically, the PERT-based methods are only used in a schedule delay analysis disadvantageously. In the scheduling diagram for mobiles such as trains, it is necessary to shift the schedule lines on the basis of existing running hour/minutes. However, she dwell time in the intermediate station also has a constraint regarding time intervals between events, such as an existing predefined dwell lime conceived as a delay absorption duration and allowance of a minimum dwell time for delay recovery. Therefore, it is also difficult to treat it in the critical path analysis of the PERT known in the art.